Properties

Label 22050bl
Number of curves $2$
Conductor $22050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 22050bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.w2 22050bl1 \([1, -1, 0, 9693, -25468619]\) \(46969655/130691232\) \(-280222000433776800\) \([]\) \(230400\) \(2.0268\) \(\Gamma_0(N)\)-optimal
22050.w1 22050bl2 \([1, -1, 0, -48240117, -128949609209]\) \(-14822892630025/42\) \(-35177510566406250\) \([]\) \(1152000\) \(2.8315\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22050bl have rank \(1\).

Complex multiplication

The elliptic curves in class 22050bl do not have complex multiplication.

Modular form 22050.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 2 q^{11} + q^{13} + q^{16} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.